A television station can only broadcast in one format at a time. All television stations have converted to digital transmission with most new programs in 16:9, and older programs in 4:3. Except for the smallest of TV markets, most stations have converted to high definitiion (HD). Typically, anything in 16:9 will be HD, which, in my opinion, is today's "standard resolution."
However, your cable or satellite provider, or an external box such as a digital converter may alter the format to make the 16:9 signals work for older 4:3 sets.
Most cable systems still consider the old lower resolution 4:3 format of NTSC as their "basic" service. Pictures for those sets are delivered in that screen ratio. To do that, they either pick a "sweet spot" from the center of the screen or deliver the 16:9 picture in "letterbox" format.
An over-the-air digital converter will downconvert the 16:9 digital (ATSC) signal to a letterboxed analog (NTSC) for your old 4:3 ratio TV sets.
On cable, if you are watching one of these "basic" channels on a 16:9 ratio set, you will not get the full picture being broadcast by the station or cable network. You need to watch a program in its original HD format to get the full benefit of the picture quality and size.
I hope I didn't confuse you!